Parameter identification and uncertainty analysis for heat transfer at the KTB drill site using a 2-D inverse method

Abstract

The German continental deep-drilling program (KTB) provided a unique opportunity for studying heat transfer processes in deep continental crust. We used an inversion technique based on the Bayesian parameter estimation to constrain parameters involved in crustal heat transfer at the KTB site and their standard deviations. Measurements in the two deep KTB boreholes and on rock material recovered from these holes were used to compile a set of a priori information for a 2-D cross-section of 40 km × 30 km. Thermal and hydraulic parameters were determined in a steady-state inverse finite-element model for a simplified geological structure. The inversion algorithm yielded a posteriori information for thermal conductivity, permeability, and heat production rate as well as for temperature and hydraulic head. Because of the large temperature range (up to 800°C), we introduced the variation of thermal conductivity with temperature into the numerical algorithm. While thermal conductivity could be well resolved, the distribution of heat production rate was relatively poorly resolved. The uncertainties for the parameters varied depending on the number of free parameters. If heat production rate was constrained tightly, the resolution of the thermal conductivity was improved. A zone of high heat production rate between 3.8 km and 10 km combined with a reduced thermal conductivity above it provided the best fit to the measured temperatures in the borehole. The steady-state inversion yielded a better solution when paleoclimatic temperature perturbations, such as those caused by the last ice age, were removed from the temperature data.